Understanding Quantum Mechanical – Thermodynamic Modelling For Surface Area And Porosity

Quantum was created to tackle a thermodynamic problem using discrete energy quanta. Quantum thermodynamics is a new research area that tries to extend classic thermodynamics and non-equilibrium statistical physics. It now also deals with the development of thermodynamic rules from quantum mechanics. The emphasis on dynamical processes out of equilibrium distinguishes it from quantum statistical mechanics.

What is Quantum theory?

Quantum theory is the foundation of contemporary physics, explaining the nature and behaviour of matter and energy at the atomic and subatomic levels. 

Quantum mechanics and quantum physics are words used to describe the nature and behaviour of matter and energy at the subatomic level.

The two founding fathers of Quantum Theory, Niels Bohr and Max Planck, won the Nobel Prize in Physics in 1921 for their work on quanta. They characterised light as quanta in the theory of the Photoelectric Effect. Albert Einstein is considered the third creator of Quantum Theory.

The Development of Quantum Theory

• Max Planck assumed that energy was made up of discrete units, or quanta, in 1900.
• Albert Einstein proposed in 1905 that not just energy but also radiation was quantized in the same way.
• Louis de Broglie suggested in 1924 that there is no fundamental difference in the constitution and behaviour of energy and matter as both can act as if they are formed of particles or waves at the atomic and subatomic levels. This idea became known as wave-particle duality, which states that elementary particles of both energy and matter act as either particles or waves depending on the circumstances.
• Werner Heisenberg claimed in 1927 that exact, simultaneous measurement of two complementary variables – such as a subatomic particle’s location and velocity – is impossible. Contrary to classical physics principles, their simultaneous measurement is inherently erroneous; the more accurately one value is measured, the more flawed the measurement of the other value will be. 

Quantum Mechanical Model

Quantum mechanics is built on the foundation of Schrödinger’s wave equation and solution. The notion of shells, subshells, and orbitals emerges from the solution of the wave equation. 

The likelihood of finding an electron at a specific location within an atom is related to the |ψ|2, where ψ denotes the electron’s wave function.

Schrödinger’s equation is difficult to apply to multi-electron atoms because the wave equation for a multi-electron atom cannot be solved correctly. Approximate strategies were used to solve this problem.

The quantum mechanical model of an atom was created when the Schrödinger wave equation was used to determine the structure of an atom.

Features of the Quantum Mechanical Model

• An electron’s energy is quantized, which means it can only have particular energy values.
• The acceptable solution of the Schrödinger wave equation is the quantized energy of an electron, which is the outcome of electrons’ wave-like characteristics.
• According to Heisenberg’s Uncertainty Principle, the precise position and momentum of an electron cannot be known. So the chance of finding an electron at a given place can be calculated with |ψ|2 at that point, where ψ represents the electron’s wave function.
• An electron’s wave function (ψ) in an atom is called an atomic orbital. When a wave function describes an electron, it occupies an atomic orbital. An electron has multiple atomic orbitals since it can have different wave functions. 
• Every wave function or atomic orbital has a specific shape and energy. 
• The orbital wave function stores all of the information about the electron in the atom, and quantum mechanics allows this information to be extracted.
• The likelihood of finding an electron at a particular site within an atom is equal to the square of the orbital wave function at that location, i.e., |ψ|2. The probability density, or |ψ|2, is always positive.

Quantum Theory of Light

1.Einstein proposed the quantum theory of light, which asserts that light travels in bundles of energy, each of which is known as a photon.

2. Each photon contains an amount of energy equal to the product of the photon’s frequency of vibration and Planck’s constant.

Planck is regarded as the founder of quantum theory. E=hv, where h is Planck’s constant, v is the frequency, and E is the energy of an electromagnetic wave, according to Planck.

Quantum Mechanical – Thermodynamic Modelling For Surface Area And Porosity

Thermodynamic models may predict features like enthalpy and phase equilibrium. Model types include equations of state, activity coefficients, empirical models, and special system-specific models.

 BET surface areas may be determined using the Dynamic Vapour Sorption (DVS) or the Inverse Gas Chromatography Surface Energy Analyzer (IGC SEA). Both tools can conduct experiments in a room and require only a tiny amount of material (typically a few milligrammes for the DVS). 

In comparison, the standard nitrogen BET approach necessitates extremely low experimental temperatures and sample quantities of typically 1 gramme. Many common materials have holes and pore networks, which can significantly influence material behaviour. 

There are several examples in nature where pores are an essential component of both live creatures and inert objects. Man-made porous materials have also recently been synthesised. Metal Organic Frameworks (MOFs), Covalent Organic Frameworks (COFs), and zeolites are examples of these. They make excellent absorbents, catalysts, and separation processes.

Conclusion

It is not easy to account for the photoelectric effect using the wave model. This effect is created when light is concentrated on specific metals and emits electrons. 

There is a minimum frequency of EM radiation for each metal at which the effect will occur. Replacing light with double the intensity and half the frequency would not create the same outcome, contrary to what would be predicted if light behaved precisely like a wave.

 The impact of light in that condition would be cumulative, meaning that the light would gradually increase until it caused electrons to be emitted. Instead, a specific minimum frequency of light triggers electron ejection. The assumption was that frequency and energy are proportionate, with higher light frequencies implying more energy. 

The minimal amount of energy that an atom may receive or lose was discovered due to this research. Max Planck gave this lowest quantity the name “quantum,” plural “quanta,” which means “how much.” One photon of light carries one quantum of energy.